The gas laws

```Vinjeru Trust School
Learning together to grow in wisdom
Vinjeru Trust School
‘The volume of a fixed mass of gas is inversely proportional to the pressure
acting on it at constant temperature.’
1
𝑉1 &times; 𝑃1 = 𝑉2 &times; 𝑃2
𝑉∞ 𝑃 at a fixed
temperature.
1
𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 &times;
𝑃
𝑉 &times; 𝑃 = constant
A quantity of gas has a volume of 9 dm3 is
under a pressure of 150 kPa. The pressure on
the gas is increased to 200 kPa while its
temperature is kept constant. What is the new
volume of the gas?
𝑉1 &times; 𝑃1 = 𝑉2 &times; 𝑃2
𝑉1 = 9 dm3
𝑃1 = 150 kPa
9 &times; 150 = 𝑉2 &times; 200
𝑉2 = ?
𝑃2 = 200 kPa
Learning together to grow in wisdom
𝑽𝟐
= 𝟔. 𝟕𝟓 𝒅𝒎𝟑
Vinjeru Trust School
‘The volume of a fixed mass of gas is directly proportional to its temperature
at constant pressure.’
𝑉∞𝑇 at a fixed
pressure.
𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 &times; 𝑇
𝑉
= constant
𝑇
𝑉1 𝑉2
=
𝑇1 𝑇2
A quantity of gas has a volume of 9 dm3 and a
temperature of 27&deg;C. If the pressure is kept
constant and the gas is heated to 52&deg;C, to what
volume will it expand?
𝑉1 𝑉2
=
𝑉1 = 9 dm3
𝑇1 𝑇2
𝑇1 = 27 + 273 = 300𝐾
9
𝑉2
=
300 325
𝑉2 = ?
𝑇2 = 52 + 273 = 325𝐾
Learning together to grow in wisdom
𝑽𝟐
= 𝟗. 𝟕𝟓 𝒅𝒎𝟑
Vinjeru Trust School
‘The pressure of a fixed mass of gas is directly proportional to its temperature
in Kelvin at constant volume.’
𝑃∞𝑇 at a fixed
pressure.
𝑃 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 &times; 𝑇
𝑃
= constant
𝑇
𝑃1 𝑃2
=
𝑇1 𝑇2
A quantity of gas has a pressure of 1 atm and a
temperature of 350&deg;C. If the volume is kept
constant, determine the pressure if the gas is
heated to 450&deg;C.
𝑃1 𝑃2
=
𝑃1 = 1 𝑎𝑡𝑚
𝑇1 𝑇2
𝑇1 = 350 + 273 = 623𝐾
1
𝑃2
=
623 723
𝑃2 = ?
𝑇2 = 450 + 273 = 723𝐾
Learning together to grow in wisdom
𝑷𝟐
= 𝟏. 𝟏𝟔 𝒂𝒕𝒎
Vinjeru Trust School
‘Boyle’s law, Charles’ law and Gay-Lussac’s law can be combined for a fixed
mass of gas. This is known as the ideal gas equation.
𝑃∞𝑇 at a fixed
pressure.
𝑃𝑉
= constant
𝑇
A gas in a container is at a pressure of 12 atm,
a volume of 23 dm3 and a temperature of 200
K. The pressure is increased to 14 atm and the
temperature is increased to 300K. What is the
new volume of the gas?
𝑃1 = 12 𝑎𝑡𝑚
𝑃1 𝑉1 𝑃2 𝑉2
=
𝑇1
𝑇2
𝑇1 = 200𝐾
𝑉1 = 23 𝑑𝑚3
𝑃2 = 14 𝑎𝑡𝑚
𝑇2 = 300𝐾
𝑉2 =?
Learning together to grow in wisdom
𝑃1 𝑉1 𝑃2 𝑉2
=
𝑇1
𝑇2
12 &times; 23 14 &times; 𝑉2
=
200
300
𝑽𝟐
= 𝟐𝟗. 𝟓𝟕𝒅𝒎𝟑
```